1,166 research outputs found
Dynamically Stable 3D Quadrupedal Walking with Multi-Domain Hybrid System Models and Virtual Constraint Controllers
Hybrid systems theory has become a powerful approach for designing feedback
controllers that achieve dynamically stable bipedal locomotion, both formally
and in practice. This paper presents an analytical framework 1) to address
multi-domain hybrid models of quadruped robots with high degrees of freedom,
and 2) to systematically design nonlinear controllers that asymptotically
stabilize periodic orbits of these sophisticated models. A family of
parameterized virtual constraint controllers is proposed for continuous-time
domains of quadruped locomotion to regulate holonomic and nonholonomic outputs.
The properties of the Poincare return map for the full-order and closed-loop
hybrid system are studied to investigate the asymptotic stabilization problem
of dynamic gaits. An iterative optimization algorithm involving linear and
bilinear matrix inequalities is then employed to choose stabilizing virtual
constraint parameters. The paper numerically evaluates the analytical results
on a simulation model of an advanced 3D quadruped robot, called GR Vision 60,
with 36 state variables and 12 control inputs. An optimal amble gait of the
robot is designed utilizing the FROST toolkit. The power of the analytical
framework is finally illustrated through designing a set of stabilizing virtual
constraint controllers with 180 controller parameters.Comment: American Control Conference 201
Keep Rollin' - Whole-Body Motion Control and Planning for Wheeled Quadrupedal Robots
We show dynamic locomotion strategies for wheeled quadrupedal robots, which
combine the advantages of both walking and driving. The developed optimization
framework tightly integrates the additional degrees of freedom introduced by
the wheels. Our approach relies on a zero-moment point based motion
optimization which continuously updates reference trajectories. The reference
motions are tracked by a hierarchical whole-body controller which computes
optimal generalized accelerations and contact forces by solving a sequence of
prioritized tasks including the nonholonomic rolling constraints. Our approach
has been tested on ANYmal, a quadrupedal robot that is fully torque-controlled
including the non-steerable wheels attached to its legs. We conducted
experiments on flat and inclined terrains as well as over steps, whereby we
show that integrating the wheels into the motion control and planning framework
results in intuitive motion trajectories, which enable more robust and dynamic
locomotion compared to other wheeled-legged robots. Moreover, with a speed of 4
m/s and a reduction of the cost of transport by 83 % we prove the superiority
of wheeled-legged robots compared to their legged counterparts.Comment: IEEE Robotics and Automation Letter
Geometric Mechanics of Contact-Switching Systems
Discrete and periodic contact switching is a key characteristic of steady
state legged locomotion. This paper introduces a framework for modeling and
analyzing this contact-switching behavior through the framework of geometric
mechanics on a toy robot model that can make continuous limb swings and
discrete contact switches. The kinematics of this model forms a hybrid shape
space and by extending the generalized Stokes' theorem to compute discrete
curvature functions called stratified panels, we determine average locomotion
generated by gaits spanning multiple contact modes. Using this tool, we also
demonstrate the ability to optimize gaits based on system's locomotion
constraints and perform gait reduction on a complex gait spanning multiple
contact modes to highlight the scalability to multilegged systems.Comment: 6 pages, 7 figures, and link to associated video:
https://drive.google.com/file/d/12Sgl0R1oDLDWRrqlwwAt3JR2Gc3rEB4T/view?usp=sharin
Real-Time Motion Planning of Legged Robots: A Model Predictive Control Approach
We introduce a real-time, constrained, nonlinear Model Predictive Control for
the motion planning of legged robots. The proposed approach uses a constrained
optimal control algorithm known as SLQ. We improve the efficiency of this
algorithm by introducing a multi-processing scheme for estimating value
function in its backward pass. This pass has been often calculated as a single
process. This parallel SLQ algorithm can optimize longer time horizons without
proportional increase in its computation time. Thus, our MPC algorithm can
generate optimized trajectories for the next few phases of the motion within
only a few milliseconds. This outperforms the state of the art by at least one
order of magnitude. The performance of the approach is validated on a quadruped
robot for generating dynamic gaits such as trotting.Comment: 8 page
Imprecise dynamic walking with time-projection control
We present a new walking foot-placement controller based on 3LP, a 3D model
of bipedal walking that is composed of three pendulums to simulate falling,
swing and torso dynamics. Taking advantage of linear equations and closed-form
solutions of the 3LP model, our proposed controller projects intermediate
states of the biped back to the beginning of the phase for which a discrete LQR
controller is designed. After the projection, a proper control policy is
generated by this LQR controller and used at the intermediate time. This
control paradigm reacts to disturbances immediately and includes rules to
account for swing dynamics and leg-retraction. We apply it to a simulated Atlas
robot in position-control, always commanded to perform in-place walking. The
stance hip joint in our robot keeps the torso upright to let the robot
naturally fall, and the swing hip joint tracks the desired footstep location.
Combined with simple Center of Pressure (CoP) damping rules in the low-level
controller, our foot-placement enables the robot to recover from strong pushes
and produce periodic walking gaits when subject to persistent sources of
disturbance, externally or internally. These gaits are imprecise, i.e.,
emergent from asymmetry sources rather than precisely imposing a desired
velocity to the robot. Also in extreme conditions, restricting linearity
assumptions of the 3LP model are often violated, but the system remains robust
in our simulations. An extensive analysis of closed-loop eigenvalues, viable
regions and sensitivity to push timings further demonstrate the strengths of
our simple controller
Robustness: a new SLIP model based criterion for gait transitions in bipedal locomotion
Bipedal locomotion is a phenomenon that still eludes a fundamental and
concise mathematical understanding. Conceptual models that capture some
relevant aspects of the process exist but their full explanatory power is not
yet exhausted. In the current study, we introduce the robustness criterion
which defines the conditions for stable locomotion when steps are taken with
imprecise angle of attack. Intuitively, the necessity of a higher precision
indicates the difficulty to continue moving with a given gait. We show that the
spring-loaded inverted pendulum model, under the robustness criterion, is
consistent with previously reported findings on attentional demand during human
locomotion. This criterion allows transitions between running and walking, many
of which conserve forward speed. Simulations of transitions predict Froude
numbers below the ones observed in humans, nevertheless the model
satisfactorily reproduces several biomechanical indicators such as hip
excursion, gait duty factor and vertical ground reaction force profiles.
Furthermore, we identify reversible robust walk-run transitions, which allow
the system to execute a robust version of the hopping gait. These findings
foster the spring-loaded inverted pendulum model as the unifying framework for
the understanding of bipedal locomotion.Comment: unpublished, in preparatio
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